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Symmetry group classification and optimal reduction of a class of damped Timoshenko beam system with a nonlinear rotational moment

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S. M. Al-Omari, F. D. Zaman, A. Y. Al-Dweik, Ryad A Ghanam

Analysis of PDEs · Submitted 20 Dec 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim An optimal system of one-dimensional subalgebras of the nonlinear damped Timoshenko system is derived for all the non-linear cases.

how it is stated · asserted 1.00 read the record →

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arXiv ID1612.06775 (version 1)
Pith IDR3TXEBEU, Pith's permanent record of this paper and its review
CitationA. Y. Al-Dweik, F. D. Zaman, Ryad A Ghanam, S. M. Al-Omari. "Symmetry group classification and optimal reduction of a class of damped Timoshenko beam system with a nonlinear rotational moment." arXiv:1612.06775 (2016). https://pith.science/paper/R3TXEBEU
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,753 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We consider a nonlinear Timoshenko system of partial differential equations (PDEs) with a frictional damping term in rotation angle. The nonlinearity is due to the arbitrary dependence on the rotation moment. A Lie symmetry group classification of the arbitrary function of rotation moment is presented. An optimal system of one-dimensional subalgebras of the nonlinear damped Timoshenko system is derived for all the non-linear cases. All possible invariant variables of the optimal systems for the three non-linear cases are presented. The corresponding reduced systems of ordinary differential equations (ODEs) are also provided.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider a nonlinear Timoshenko system of partial differential equations (PDEs) with a frictional damping term in rotation angle. background 0.72 0.68 0.04 asserted 0.96
s1 The nonlinearity is due to the arbitrary dependence on the rotation moment. background 0.91 0.18 0.03 asserted 1.00
s2 A Lie symmetry group classification of the arbitrary function of rotation moment is presented. contribution 0.78 0.93 0.15 asserted 1.00
s3 An optimal system of one-dimensional subalgebras of the nonlinear damped Timoshenko system is derived for all the non-linear cases. contribution 0.58 0.96 0.29 asserted 1.00
s4 All possible invariant variables of the optimal systems for the three non-linear cases are presented. result 0.84 0.93 0.14 asserted 0.99
s5 The corresponding reduced systems of ordinary differential equations (ODEs) are also provided. result 0.77 0.94 0.17 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider a nonlinear Timoshenko system of partial differential equations (PDEs) with a frictional damping term in rotation angle. The nonlinearity is due to the arbitrary dependence on the rotation moment. A Lie symmetry group classification of the arbitrary function of rotation moment is presented. An optimal system of one-dimensional subalgebras of the nonlinear damped Timoshenko system is derived for all the non-linear cases. All possible invariant variables of the optimal systems for the three non-linear cases are presented. The corresponding reduced systems of ordinary differential equations (ODEs) are also provided.

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